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STRING THEORY AND M-THEORY

A MODERN INTRODUCTION

String theory is one of the most exciting and challenging areas of modern

theoretical physics. This book guides the reader from the basics of string

theory to very recent developments at the frontier of string theory research.

The book begins with the basics of perturbative string theory, world-sheet

supersymmetry, space-time supersymmetry, conformal field theory and the

heterotic string, and moves on to describe modern developments, including

D-branes, string dualities and M-theory. It then covers string geometry

(including Calabiâ€“Yau compactifications) and flux compactifications, and

applications to cosmology and particle physics. One chapter is dedicated

to black holes in string theory and M-theory, and the microscopic origin

of black-hole entropy. The book concludes by presenting matrix theory,

AdS/CFT duality and its generalizations.

This book is ideal for graduate students studying modern string theory, and it

will make an excellent textbook for a 1-year course on string theory. It will also

be useful for researchers interested in learning about developments in modern

string theory. The book contains about 120 solved exercises, as well as about 200

homework problems, solutions of which are available for lecturers on a pass-

word protected website at www.cambridge.org/9780521860697.

K A T R I N B E C K E R is a Professor of physics at Texas A & M University. She

was awarded the Radcliffe Fellowship from Harvard University in 2006 and

received the Alfred Sloan Fellowship in 2003.

M E L A N I E B E C K E R is a Professor of physics at Texas A & M University. In

2006 she was awarded an Edward, Frances and Shirley B. Daniels Fellowship

from the Radcliffe Institute for Advanced Studies at Harvard University. In

2001 she received the Alfred Sloan Fellowship.

J O H N H . S C H W A R Z is the Harold Brown Professor of Theoretical Physics

at the California Institute of Technology. He is a MacArthur Fellow and a

member of the National Academy of Sciences.

This is the first comprehensive textbook on string theory to also offer an up-to-

date picture of the most important theoretical developments of the last decade,

including the AdS/CFT correspondence and flux compactifications, which

have played a crucial role in modern efforts to make contact with experiment.

An excellent resource for graduate students as well as researchers in high-

energy physics and cosmology.

Nima Arkani-Hamed, Harvard University

An exceptional introduction to string theory that contains a comprehensive

treatment of all aspects of the theory, including recent developments. The clear

pedagogical style and the many excellent exercises should provide the interested

student or researcher a straightforward path to the frontiers of current research.

David Gross, Director of the Kavli Institute for Theoretical Physics, University of

California, Santa Barbara and winner of the Nobel Prize for Physics in 2004

Masterfully written by pioneers of the subject, comprehensive, up-to-date and

replete with illuminating problem sets and their solutions, String Theory and

M-theory: A Modern Introduction provides an ideal preparation for research

on the current forefront of the fundamental laws of nature. It is destined to

become the standard textbook in the subject.

Andrew Strominger, Harvard University

This book is a magnificient resource for students and researchers alike in the

rapidly evolving field of string theory. It is unique in that it is targeted for

students without any knowledge of string theory and at the same time it

includes the very latest developments of the field, all presented in a very fluid

and simple form. The lucid description is nicely complemented by very instruc-

tive problems. I highly recommend this book to all researchers interested in the

beautiful field of string theory.

Cumrun Vafa, Harvard University

This elegantly written book will be a valuable resource for students looking for

an entry-way to the vast and exciting topic of string theory. The authors have

skillfully made a selection of topics aimed at helping the beginner get up to

speed. I am sure it will be widely read.

Edward Witten, Institute for Advanced Study, Princeton,

winner of the Fields Medal in 1990

STRING THEORY AND M-THEORY

A Modern Introduction

KATRIN BECKER,

Texas A & M University

MELANIE BECKER,

Texas A & M University

and

JOHN H. SCHWARZ

California Institute of Technology

cambridge university press

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, SÃ£o Paulo

Cambridge University Press

The Edinburgh Building, Cambridge cb2 2ru, UK

Published in the United States of America by Cambridge University Press, New York

www.cambridge.org

Information on this title: www.cambridge.org/9780521860697

Â© K. Becker, M. Becker and J. H. Schwarz 2007

This publication is in copyright. Subject to statutory exception and to the provision of

relevant collective licensing agreements, no reproduction of any part may take place

without the written permission of Cambridge University Press.

First published in print format 2006

978-0-511-25653-0 eBook (EBL)

isbn-13

isbn-10 0-511-25653-1 eBook (EBL)

978-0-521-86069-7 hardback

isbn-13

0-521-86069-5 hardback

isbn-10

Cambridge University Press has no responsibility for the persistence or accuracy of urls

for external or third-party internet websites referred to in this publication, and does not

guarantee that any content on such websites is, or will remain, accurate or appropriate.

v

To our parents

vi

An Ode to the Unity of Time and Space

Time, ah, time,

how you go oï¬€ like this!

Physical things, ah, things,

so abundant you are!

The Ruoâ€™s waters are three thousand,

how can they not have the same source?

Time and space are one body,

mind and things sustain each other.

Time, o time,

does not time come again?

Heaven, o heaven,

how many are the appearances of heaven!

From ancient days constantly shifting on,

black holes ï¬‚aring up.

Time and space are one body,

is it without end?

Great indeed

is the riddle of the universe.

Beautiful indeed

is the source of truth.

To quantize space and time

the smartest are nothing.

To measure the Great Universe with a long thin tube

the learning is vast.

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